Download Acids and Bases

self study
Most of this is probably background from a prior chemistry course;
some near the end is GG325 review
Aqueous Inorganic Geochemistry of
Natural Waters
Three important topics:
1. Acids, bases and the aqueous CO2 system
2. Behavior of ions in aqueous solution
3. Quantifying aqueous solubility and total dissolved solids
(TDS)
Pease read Manahan chapter 3 and review chapter 28 (6th Ed) for next week
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Acids and Bases
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1. Two Types of Acids and Bases:
a. Brönstead acids and bases contain H+ and OHHCl ↔ H+ + + Cl- (acid)
NaOH ↔ Na+ + OH- (base).
water is acid and base simultaneously, H2O ↔ H+ + OH-.
pure water and acid neutral aqueous solutions have equal
amounts of H+ and OH-.
b. Lewis acids and bases
Brönstead acids can be thought of as electron deficient ions
and bases as electron excessive ions, which provides a
different perspective on acidity/basisity that we can extend to
other (non protic and non hydroxyl) compounds. We call this
the Lewis acid/base concept.
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Brönstead acidity:
Kw is the equilibrium constant for the dissociation of water.
H2O ↔ H+ + OHKw = [H+][OH-] = 10-14 at 25EC
Kw has a slight temperature dependence:
Temp (EC)
0
25
60
Kw
10-14.94
10-14
10-13.02
less dissociated
more dissociated
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Brönstead acidity:
H2O ↔ H+ + OHKw = [H+][OH-]
An acid neutral solution always has [H+] = [OH-].
Setting [H+] = x, yields x2= 10-14
x = 10-7 = moles of H+ in this solution.
pH = -log aH+ ~ -log [H+]
pH = -log [10-7] = 7 in an acid neutral at 25°C
A less common but sometimes useful variable is:
pOH = -log aOH-~ -log [OH-]
In an acid neutral solution pOH = pH = 7
In any water at 25EC, pH + pOH = 14
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Lewis Acids and Bases
Lewis acid example:
BF3
BF3 has an empty orbital on B and only 6 electrons involved in
the 3 B-F bonds. It is electron deficient so it is known as a
Lewis Acid (B needs 2e- to achieve a Ne electronic
configuration).
BF3 will react with H2O to get its needed electrons, creates
new ions, and acidify the solution acid in a Brönstead sense.
BF3 + H2O ↔ [OH-BF3]- + H+
Lewis base example:
NH3
In a similar fashion, NH3 (Ammonia) can be shown to be a
lewis base, such that
NH3 + H2O ↔ [H-NH3]+ + OHGG425 Wk2, S2016
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Aqueous acid-base relationships
Neutral pH = 7
"low" pH is <7 = acid solution = large H+
"high" pH is >7 = base solution = small H+
How much do natural waters deviate from acid neutrality?
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The aqueous CO2 system
Equilibria involving carbon dioxide and its conjugate bases in
water set the baseline pH of almost all natural waters at the
Earth's surface
other constituents usually serve to alter this carbonate equilibrium
pH.
Environmental chemists often speak of ∑ CO2(aq) = aqueous
carbon dioxide in all of its aqueous forms.
First, let’s show that the amount of CO2 present in the atmosphere
and the pH (= -log[H+]) of water in equilibrium with it are linked,
.. as is the solubility of CaCO3 as [Ca2+(aq)] .
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Example: Combining Equilibria in the aqueous CO2 system
Let's combine the system of inorganic reactions governing the amount
of dissolved CO2 in natural waters (which bears directly on the amount
of CO2 in our atmosphere, geosphere and biosphere)
CO2 has 4 forms in water, which are related by a series of chemical;
reactions shown schematically in the figure below:
a. dissolved gaseous carbon dioxide
CO2(aq)
b. carbonic acid
H2CO3(aq)
c. bicarbonate anion
HCO3-(aq)
d. carbonate anion
CO32-(aq)
Note that CaCO3 formation (by
inorganic precipitation or biogenic
precipitation) is the primary upper
limit control on dissolved carbon
dioxide concentration
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The 4 forms of CO2 in water are related by 5 chemical
reactions:
(disregarding for now photosynthesis/respiration)
1. CO2(g) ↔ CO2(aq)
This is a gas solubility reaction (sometimes called a Henry's law reaction. K is
given the subscript "H": KH
2. CO2 (aq) + H2O ↔ H2CO3(aq)
This is a bond reorganization reaction. It is also a type of hydration (reaction with
water). K = Keq (no "special" nomenclature)
3. H2CO3 (aq) ↔ HCO3-(aq) + H+
An acid dissociation reaction. Commonly given equilibrium constant notations of
Ka if it is a monoprotic acid, or Ka1 for the first acid dissociation of a polyprotic acid
4. HCO3- (aq) ↔ CO32- (aq) + H +
Another acid dissociation reaction. This is the second dissociation of dioprotic
carbonic acid, so we call it or Ka2.
5. CaCO3 (s) ↔ Ca2+ (aq) + CO32- (aq)
This is a solubility/dissolution reaction. K is Ksp .
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Many texts use the simplifying assumption that reactions "2"
and "3" can be combined since little free H2CO3(aq) is found
in natural waters.
Because of this last point, the reaction sequence is
shortened to
1. CO2(g) ↔ CO2(aq)
KH
2. CO2(aq) + H2O ↔ HCO3-(aq) + H+
K'a1
3. HCO3-(aq) ↔ CO32-(aq) + H+
Ka2
4. CaCO3(s) ↔ Ca2+(aq) + CO32-(aq)
Ksp
Let's mathematically combine them to determine an expression for the
CaCO3 solubility in a natural water (in terms of [Ca2+(aq)]). The water is
open to gas exchange with the atmosphere and we assume there are no
other reactions affecting Ca2+, H+ or Σ CO2 (aq) (carbon dioxide in all of
its aqueous forms).
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It’s all algebra…
Working backward from reaction 4: Ksp = [Ca2+]·[CO32-]
we can rearrange to:
[Ca2+] = Ksp/[CO32-] A.
from reaction 3:
Ka2= [H+]·[CO32-]/[HCO3-]
we can rearrange to:
[CO32-] = Ka2 [HCO3-]/[H+]
2+
substituting into A. gives: [Ca ]= Ksp·[H+]/Ka2·[HCO3-] B.
the same type of rearrangement of equation 2 in terms of [HCO3-] yields:
[HCO3-] = K'a1·[CO2(aq)]/[H+]
2+
+
+
substituting into B. gives: [Ca ]= Ksp·[H ]·[H ]/Ka2·K'a1·[CO2(aq)] C.
Finally rearrangement of eqution1
gives:
substituting into C. gives:
KH = [CO2(aq)]/PCO2
PCO2 = KH·[CO2(aq)] D.
[Ca2+(aq)] =
Ksp · [H+]2
KH · K'a1· Ka2 · PCO2
What does this equation tell us? [Ca2+(aq)] will depend on the amount of CO2 present
in the atmosphere and the pH (= -log[H+]) of the water. We will discuss the absolute
values of these equilibrium constants and the predictions that can be made with the
expressions on this page later in the semester.
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Let's now examine the pH relationships in a mixture of just water and CO2
components, meaning we ignore for now the effects of CaCO3
precipitation/dissolution. The Bjerrum plot shows dissolved CO2, HCO3- and CO32as a function of pH The curves are drawn using equations from last lecture.
Log ai
0
maximum buffering capacity
pH=6.35
pH=10.33
2HCO3
CO3
H2CO3
-2
H+
OH-
-4
-6
1
3
5
7
9
11
13
pH
1st end point pH=4.32
2nd end point pH=8.35
minimum buffering capacity
Bjerrum plot, activities of different species
in the aqueous carbonate system as a
function of pH, for ΣCO2 = 10-2, T = 25°C.
Note that one of these 3 chemical species essentially dominates the mixture in
each of three domains, which are separated by vertical lines at values of pH =
pKa1 and pH = pKa2. These vertical lines are the locus of maxima in buffering
capability of the solution.
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What is "buffering capacity"?
It is the ability of a solution to withstand acid or base
addition and remain at or near the same pH.
It occurs when the concentrations of acid and conjugate
base are very similar.
Anti bufferingness?
Aqueous acid solutions are least buffered at the
endpoints because the concentrations of acid and
conjugate base are most different, so that their ratio is
sensitive to slight changes in pH.
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This and the following slide look at a buffering capacity of an aqueous
solution containing a weak monoprotic acid like acetic acid:
CH3COOH ↔ H+ + CH3COO-
(in shorthand: H-Ac ↔ H+ + Ac-)
Ka = [H+][Ac-]/[H-Ac]
a. take the -log of both sides of the Ka expression: -log Ka= - log[H+] log[Ac-]/[H-Ac]
b. rearrange
pKa-pH = - log [Ac-]/[H-Ac]
c. move sign
pH-pKa = log [Ac-]/[H-Ac]
Remember, pKa is a constant at a given P and T.
K To get pH knowing [Ac-]/[H-Ac] and pKa,
pH = pKa + log [Ac-]/[H-Ac]
rearrange c
K To get [A-]/[HA] knowing pH and pKa,
10pH-pKa = [Ac-]/[H-Ac]
get rid of log in c
To solve for [Ac-] and [H-Ac], you need the total amount of acidic substance
in the solution:
∑[H-Ac]=[Ac-] + [H-Ac]
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K In general when we add "x" mol/L acid (H+) to a solution of H-Ac in water, the pH
changes and [Ac-]/[HAc] changes to [Ac- - x]/[HAc + x].
Acetic Acid
1
10
0.1
0.01
When [Ac-]/[HAc] is close to 1 (i.e.
at pH = pKa), the solution is less
sensitive to the added x so the
solution is buffered at pH = pKa.
At [Ac-]/[HAc] <1 or > 1, the
solution is not buffered.
0.001
0.0001
1E-05
ph=pKa
1E-06
1
0
2
4
6
pH
8
10
A plot of the pH sensitivity of an acetic acid solution
as an external strong acid is added shows that near
pHm = pKa, )pH/mol H+ added is at a minimum
You can reason through the maximum and minimum buffering cases for CO2 in water
yourself using:
H2CO3 : H+ + HCO3-
Ka1 = [H+][HCO3-]/[H2CO3] pKa1 = pH - log [HCO3-]
[H2CO3]
HCO3- : H+ + CO32-
Ka2 = [H+][CO32-]/[HCO3-]
pKa2 = pH - log [CO32-]
[HCO3-]
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Acetic Acid
1
10
0.1
0.01
0.001
0.0001
1E-05
ph=pKa
1E-06
1
0
2
4
6
8
10
pH
Oxides of metals
Bond character and Lewis
Acid/Base concepts help us
understand how metal oxides
will react in the hydrosphere.
Basic Oxides
These are ionic oxides.
Example: Na2O. In a compound
where O has its e- held tightly to
itself in a highly electronegative bond
with a metallic element (little sharing),
O2- ions are typically produced upon reaction with water; O2- ions will react to take
an H+ from H2O leaving two OH- in its wake (and therefore a basic solution).
Acid Oxides
These are covalent oxides. Example: (SiO2)
When O is in a more covalent bond the "metal" shares more of the e-. To be stable
in dissociated form in water, both elements in the bond try to get an electron by
dissociating water and taking an OH- ion out of circulation. This leave an excess of
H+ (an acid solution).
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pH Summary
K pH is a function of the ratio of conjugate base/acid.
K buffered: when acid and conjugate base are close to equal,
log(conjugate base/acid) goes to 0 and pH=pKa.
K deviating from this point, each mole of H+ added or subtracted
goes into changing (conjugate base/acid).
Kcontinue to change pH and approach an endpoint, this ratio
changes more with each successive unit of pH change because
almost all of the acid or conjugate base is consumed.
K oxides of elements can be thought of as Lewis acids and bases
based on their bond character with O, and will make water acidic
or basic accordingly
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Alkalinity
the acid-neutralizing capacity of an aqueous solution
K It is the sum of all the titratable bases in solution that can be
neutralized with strong acid.
K Alkalinity is a significant environmental variable for natural
waters and waste waters.
K The alkalinity of many natural waters is primarily a function
of ∑CO2(aq) and OH-.
[Alk] ≈ [HCO3-] + 2[CO32-] + [OH-] - [H+]
K But the measured value can also include contributions from
borates, phosphates, organic acid anions, silicates or other
bases if present.
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Aqueous Solubility
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2. Behavior of ions in water:
Aqueous stability of ions is the primary determinant of the "distribution" of many
elements between solids (minerals and organic matter) and water in surficial
environments.
The form that the ion takes in aqueous solution is the fundamental control on
element solubility.
Form is mostly a function of how the ion interacts with water molecules (as well as
OH-, H3O+ and dissolved oxygen, aka “DOx”).
These interactions are essentially dictated by Ion-O bonding characteristics,
particularly in very fresh waters.
During hydration (lewis acid/base interaction with H2O molecules),
Electronegativity
and
ion size
determine the bonding preference of a cation for DOx or water (and its conjugate
bases: OH-, O2-)
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Behavior of ions in water
Cation electronegativity determines how "ionic" or "covalent"
the resulting O-cation "bonds" is:
electropositive elements make ionic "bonds" whereas
electronegative elements make relatively covalent
"bonds".
Un-hydrated ion size affects O-cation ligand "bond
character" and the stability of the hydration complex, since
the geometric "fit" of electrons in "bonds" worsens as cation
size increases.
Cations that can form a stable covalent bond with O will do
so in water. Those that don’t will make ionic bonds.
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Behavior of ions in water
The relative solubility of the cation-oxygen compound
depends on the relative stability in water of the resulting
oxy- or hydroxy ion versus a solid composed of the original
cation and oxygen.
For instance, the product would be favored in the reaction
below for more covalent X-O bonds. Note that as H+ is
released the water becomes acidic.
Arrows depict the flow of electrons in breaking the H-O and forming the X-O bonds
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Behavior of ions in water
Elements in green are largely insoluble
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Behavior of ions in water - Ionic Potential
(= charge divided by radius) is very useful for quantifying this behavior.
{ Intermediate IP ions (~ 4 -10):
generally the least water soluble.
{ Low IP ions: take positive charges
in solution (ionic interaction with O in
water)
{ High IP ions: take negative
charges in solution (covalent
interaction with O in water, such that
the number of electrons donated by
oxygen atoms exceeds the original
+n charge of the raw cation, making
an anion).
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Behavior of ions in water
The previous discussion notwithstanding, other aspects of
aqueous solution chemistry can also affect an ion's
solubility through similar Lewis acid-base type interactions.
X-Y interactions, where Y is something other than X-O, as
well as ion-ion interactions (X1 - X2) can be rationalized
using similar arguments, as we will see during this course.
Such effects become particularly pronounced in very saline
waters and/or water enriched in dissolved organic
substances.
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Solubility Summary
↑
in pure water, elements on the extreme left and right
sides of the Periodic Chart tend to be more soluble than
those in the center.
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Solubility Summary - 2
↓
the solubility of elements in the chart’s center is low in
pure water, but can be enhanced by other dissolved
constituents found in more complex aqueous solutions.
This is particularly true when the water contains dissolved organic carbon (DOC)
compounds (which typically contain reactive O atoms).
The presence or absence or dissolved organic matter often determines whether or
not many heavy metals are soluble (and thus mobile) in a particular environment.
An additional complicating factor in natural systems that we will discuss at length this
semester is that water often comes with various sorts of particles (which also contain
Lewis bases of O and/or other Y).
Thus, when X interacts with O or Y that are attached to a solid, X becomes part of
the suspended phase
and when it interacts with O or Y on a dissolved material, X is part of the dissolved
phase.
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complexation/chelation reactions in
aqueous solution chemistry
Definition
A complex is an association of molecules in solution or at a
particle surface where electrons sharing occurs through
associations that are weaker than true chemical bonds but
none the less strong enough to make identifiable substances.
The Lewis Acid-Base "donor/acceptor" concept is handy here,
because complexes involve stabilization of charge (or partial
charge) on ions (or polar molecules) through electron sharing.
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complexation/chelation
Complexes involve ligands and host ions.
We will mostly consider complexes of cations (M+n) and
electron donor ligands.
As discussed in lecture 3, Hydration is a specific type of
complexation reaction where the ligands are all water:
Fe2+ + 6H2O ↔ Fe(H2O)62+
Schematic depiction of water using it’s lone pairs
of electrons to stabilize an Fe2+ ion in solution.
The hydrate itself involves 5 other water molecules.
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ligands:
Other common natural ligands are Cl- (chloride) and :NH3 (ammonia).
These, along with water, are known as unidentate.
Unidentate ligands offer electrons from a single site to a complex.
In an aqueous Fe+3 solution with both Cl- and :NH3, many complexes are
possible involving these two ligands and H2O.
The charge on the complex remains unchanged relative to Fe+3 with H2O
and NH3 ligands but each Cl- ligand brings one negative charge.
All of the following complexes are possible in this solution:
[FeCl6]-3 [FeCl3(NH3)3]0 [FeCl2(NH3)4]+ [Fe(NH3)6]+3
The relative proportions of these complexes will vary with pH since
NH3 + H+ ↔ NH4+.
Thus [FeCl6]-3 would be favored at low pH
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ligands:
Chelation involves complexation by multidentate ligands.
Unidentate ligands are individual ligands that have more than one
electron or electron pair to donate to a cation.
A bidentate ligand has two active binding sites for a cation
e.g., ethylene di-amine, :NH2-CH2-CH2-H2N:
and oxalic acid/oxylate anion, which has the following forms in solution:
OO
-
OO
OO
-
HO-C-C-OH <----> HO-C-C-O <----> HO-C-C-O
OO
<----> - O-C-C-O - <---->
Carbon-oxygen double bond
O O
O-C-C-O
delocalized e- in π bond
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Hydrocarbon chain
short hand
ligands:
Bidendate ligands can bind in two ways:
Cl
Cl
N
N
Cl
Cl
M
M
Cl
Cl
N
Cl
Cl
cis
trans
next to
across
N
a "small" bidentate ligand such as ethylene diamine can usually only
bind cis for geometric reasons.
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Chelates are an important control of ionic concentration in
solution.
In cases where multidentate ligands are present in natural or
waste waters, they can actually leach metal ions from solids
(like pipes or rocks) into solution.
Humic Substances are an important class of naturally occurring
organic chelating agents; We discuss them later.
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Why are Chelates favored over Complexes with similar
electron donors in the ligands?
We can understand this phenomenon with thermodynamic reasoning (i.e.,
estimates of Gibbs free energy and Keq should favor the chelate).
Recall that ∆G° = ∆H° -T∆S°
Example 1
Compare a metal di-amino complex (two ammonia ligands) vs a metal
complex with ethylene di-amine (two ammonia molecules “fused” onto a
single ethylene molecule, making it a bidentate ligand)
From a bond energy perspective, the M-N electron donor/acceptor
relationship is very similar for
H3N---M---NH3
and
M
.
NH2CH2CH2NH2
the M-N electron donor/acceptor relationship has very similar bond energy
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Energetics of Chelates vs. Complexes
H3N---M
and
M
similar bond energy means ∆Hformation is similar.
NH2CH2CH2NH2
But ∆Sformation differs for both…
because it takes 2 NH3 ligands and 1 metal ion to come together to make
H3N---M---NH3 (more order)
but it takes only 2 entities (1 ethylene diamine ligand and 1 metal ion) to
come together to make the metal chelate (less order).
∆Sreaction is positive for chelate formation relative to the ammonia.
∆H° ~ 0, so ∆G° = -T∆S°, @ constant T, ∆G° = -∆S°.
Since ∆G° is negative, Keq >1 and products are favored as written.
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Energetics of Chelates vs. Complexes
Example 2
What about a di-amino quadro-chloro metal complex vs an ethylene
diamine quadro-chloro chelate?
Again, ∆S is positive for chelate formation relative to the di-unidentate
ammonia metal complex. So ∆Gformation of the chelate is more negative (and
thus favored)
Cl
Cl
2NH
Cl
N +
3
Cl
NH N
3
CH
M
2
M
+ CH2 <--->
CH
2
CH
Cl
2
NH3
N
Cl N
Cl
Cl
2 molecules
3 molecules
∆S is positive ---------->
∆G° = -∆S° , so products are favored as written.
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Quantifying
Aqueous Solubility
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3. Quantifying aqueous solubility
Solubility refers to the equilibrium quantity of a substance
that can be dissolved in a solution.
We can put lots of high solubility material but only a little of a
low solubility material into a solute at saturation.
Saturation = maximum solute concentration in solution.
Concentrations are given in units of molarity (mole/L),
molality (mole/kg), ppm by weight (or mg/kg = µg/g)
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How stuff dissolves also matters:
Before we can quantify saturation and use equilibrium
constant expressions to predict solubilities of materials in
water, we need to consider the dissolution process itself.
Two types of dissolution reactions exist:
1. Congruent – all of a material goes into solution, leaving
nothing behind when it is dissolved
2. Incongruent – parts of a material go into solution, leaving a
new, modified material behind.
These terms refer to the undissolved solid left behind
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There are also different type of solutes in solution:
1. ionically bonded solids, which dissociate upon dissolution to
form ions.
NaCl (s) ↔ Na+ (aq) + Cl- (aq)
2. covalently bonded material which go into solution essentially
unchanged, such as glucose .
C6H12O2 (s) ↔ C6H12O2 (aq)
3. covalently or ionically bonded materials which undergo a
reaction with the solvent
CO2 (g) ↔ CO2 (aq) ↔ HCO3- (aq) + H+ (aq)
MgSiO3 (s) + H2O ↔ Mg2+ (aq) + SiO2(aq) + 2 OH- (aq)
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We define solubility somewhat differently for each type of solute.
In general, solubility is a mole-for-mole measure of how much of a solid
will go into a given volume of solution, regardless of what happens to it
once it is there.)
Ionic salts
NaCl (s) ↔ Na+ (aq) + Cl- (aq)
each mole of halite, NaCl (s), that dissolves in a given volume of water
produces one mole of Na+ (aq) and one mole of Cl- (aq).
The solubility is defined as the moles of NaCl (s) that will dissolve into a
given volume of solution at saturation, which equals [Na+] which equals
[Cl-]
We have already defined Ksp = [Na+][Cl-]
So, setting x =[Na+]=[Cl-] =solubility, and using Ksp = x2
we find that
Solubility = x = Ksp½.
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What about cases for ionic solids that don’t produce solutes on a one to
one mole basis?
For instance, fluorite (CaF2) dissolves as follows
CaF2 (s) ↔ Ca2+ (aq) + 2F- (aq)
In this case, it is easier to define solubility in terms of Ca2+ (aq) since one
mole of fluorite dissolves to make one mole of calcium ions.
Solubility = x = [Ca2+]
We also see that solubility = ½ [F-], since 2 moles of fluoride are
produced for each mole of solid dissolved.
How is solubility (again as "x") related to Ksp?
Ksp = [Ca2+][F-]2
since [F-] = 2[Ca2+]
Ksp = x • (2x) 2 = 4x3
Solubility =x = (Ksp/4)1/3
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For covalently bonded solids:
C6H12O2 (s)
↔
K = [C6H12O6]
C6H12O2 (aq)
and x = k
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An important congruent dissolution reaction in nature is the
dissolution of pyroxene minerals :
MgSiO3 (s) + 3 H2O ↔ Mg2+ (aq) + H4SiO4 (aq) + 2 OH- (aq)
Sometimes written as:
MgSiO3 (s) + H2O ↔ Mg2+ (aq) + SiO2(aq) + 2 OH- (aq)
In either event, 1 mole of enstatite, MgSiO3 (s), dissolves to
produce:
O 1 mole of Mg2+ (aq)
O 1 mole of dissolved Si as either “SiO2(aq)” or “H4SiO4(aq)”
O 2 moles of OH- (aq).
Solubility = x = [Mg2+] = [SiO2(aq)] = ½ [OH- (aq)]
K = [Mg2+] [SiO2 (aq)] [OH-]2
K = x x (2x)2 = 4x4
and X = (K/4)¼
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The same logic applies to incongruent dissolution reactions
For a solid that reacts with water upon dissolution to make a new
solid, we define solubility based upon a resulting solute that is easily
related back to the original substance being dissolved (if possible).
We could also define the solubility based on the proportion of
modified to unmodified substance in the undissolved state.
An important incongruent dissolution that occurs during chemical
weathering and soil formation is:
2KAlSi3O8 +2H+ + H2O ↔ Al2Si2O5(OH)4 + 2K+ + 4SiO2(aq)
solid K-feldspar & water reacting to produce solid Kaolinite, dissolved silica, & potassium ions
1 mole of K-feldspar dissolves to produce 1 mole of K+.
We define solubility using [K+] at saturation.
solubility = x = [K+] = ½ [SiO2(aq)]
solubility also = - [H+] (hydrogen ions consumed)
GG425 Wk2, S2016
K The common ion effect.
In complex solutions this tends to lower the expected
solubility of a salt relative to that in pure water.
For example..
both NaCl and CaCl2 produce Cl- ions upon dissolution.
The solubility of NaCl can be written as x = [Cl-]
The solubility of CaCl2 can be written as x = ½ [Cl-].
The solubility of NaCl and CaCl2 in a solution of both
depends on each other, due to the common Cl- ion.
GG425 Wk2, S2016
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